A random sample of n 1 20winter days in Denver gave a sample mean pollution index x 1 43 Previous studies show that 1 11 For Englewood (a suburb of Denver), a random sample of n 2 12winter days gave a sample mean pollution index of x 2 36 Previous studies show that 2 13 Assume the pollution index is normally distributed in both Englewood and Denver Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter Use a 1 level of significance What is the value of the sample test statistic (Test the difference 1 2 Round your answer to two decimal places ) (c) Find (or estimate) the P value (Round your answer to four decimal places ) Q2 A Michigan study concerning preference for outdoor activities used a questionnaire with a six point Likert type response in which 1 designated not important and 6 designated extremely important A random sample of n 1 48adults were asked about fishing as an outdoor activity The mean response was x 1 4 9 Another random sample of n 2 50adults were asked about camping as an outdoor activity For this group, the mean response was x 2 5 5 From previous studies, it is known that 1 1 5and 2 1 2 Does this indicate a difference (either way) regarding preference for camping versus preference for fishing as an outdoor activity Use a 5 level of significance Note A Likert scale usually has to do with approval of or agreement with a statement in a questionnaire For example, respondents are asked to indicate whether they strongly agree, agree, disagree, or strongly disagree with the statement a) What is the value of the sample test statistic (Test the difference 1 2 Round your answer to two decimal places ) b) Find (or estimate) the P value (Round your answer to four decimal places ) Q3 A random sample of n 1 10 regions in New England gave the following violent crime rates (per million population) x 1 New England Crime Rate 3 53 94 24 13 34 11 84 82 93 1 Another random sample of n 2 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population) x 2 Rocky Mountain Crime Rate 3 74 14 75 53 34 83 52 43 13 55 22 8 Assume that the crime rate distribution is approximately normal in both regions (a) Use a calculator to calculate x 1 , s 1 , x 2 , and s 2 (Round your answers to four decimal places ) x 1 s 1 x 2 s 2 What is the value of the sample test statistic (Test the difference 1 2 Round your answer to three decimal places ) Q4 In this problem, assume that the distribution of differences is approximately normal Note For degrees of freedom d f not in the Student's t table, use the closest d f that is smaller In some situations, this choice of d f may increase the P value by a small amount and therefore produce a slightly more conservative answer Are America's top chief executive officers (CEOs) really worth all that money One way to answer this question is to look at row B , the annual company percentage increase in revenue, versus row A , the CEO's annual percentage salary increase in that same company Suppose a random sample of companies yielded the following data B Percent increase for company 24 25 25 18 6 4 21 37 A Percent increase for CEO 21 23 24 14 4 19 15 30 Do these data indicate that the population mean percentage increase in corporate revenue (row B ) is different from the population mean percentage increase in CEO salary Use a 5 level of significance (Let d B A ) What is the value of the sample test statistic (Round your answer to three decimal places ) Q5 In this problem, assume that the distribution of differences is approximately normal Note For degrees of freedom d f not in the Student's t table, use the closest d f that is smaller In some situations, this choice of d f may increase the P value by a small amount and therefore produce a slightly more conservative answer At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below Weather Station 1 2 3 4 5 January 135 120 126 64 78 April 108 115 100 88 61 Does this information indicate that the peak wind gusts are higher in January than in April Use 0 01 (Let d JanuaryApril ) What is the value of the sample test statistic (Round your answer to three decimal places ) Q6 In this problem, assume that the distribution of differences is approximately normal Note For degrees of freedom d f not in the Student's t table, use the closest d f that is smaller In some situations, this choice of d f may increase the P value by a small amount and therefore produce a slightly more conservative answer In environmental studies, sex ratios are of great importance Wolf society, packs, and ecology have been studied extensively at different locations in the U S and foreign countries Sex ratios for eight study sites in northern Europe are shown below Location of Wolf Pack Males (Winter) Males (Summer) Finland76 57 Finland51 54 Finland71 55 Lapland55 48 Lapland64 55 Russia50 50 Russia41 50 Russia55 45 What is the value of the sample test statistic (Round your answer to three decimal places )

Question

A random sample of n 1  20winter days in Denver gave a sample mean pollution index x 1  43  Previous studies show that 1  11  For Englewood (a suburb of Denver), a random sample of n 2  12winter days gave a sample mean pollution index of x 2  36  Previous studies show that 2  13  Assume the pollution index is normally distributed in both Englewood and Denver  Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter  Use a 1  level of significance  What is the value of the sample test statistic  (Test the difference 1 2   Round your answer to two decimal places ) (c) Find (or estimate) the P  value  (Round your answer to four decimal places ) Q2 A Michigan study concerning preference for outdoor activities used a questionnaire with a six point Likert type response in which 1 designated  not important  and 6 designated  extremely important   A random sample of n 1  48adults were asked about fishing as an outdoor activity  The mean response was x 1  4 9  Another random sample of n 2  50adults were asked about camping as an outdoor activity  For this group, the mean response was x 2  5 5  From previous studies, it is known that 1  1 5and 2  1 2  Does this indicate a difference (either way) regarding preference for camping versus preference for fishing as an outdoor activity  Use a 5  level of significance  Note   A Likert scale usually has to do with approval of or agreement with a statement in a questionnaire  For example, respondents are asked to indicate whether they  strongly agree,   agree,   disagree,  or  strongly disagree  with the statement  a) What is the value of the sample test statistic  (Test the difference 1 2   Round your answer to two decimal places ) b) Find (or estimate) the P  value  (Round your answer to four decimal places ) Q3 A random sample of n 1   10 regions in New England gave the following violent crime rates (per million population)  x 1  New England Crime Rate 3 53 94 24 13 34 11 84 82 93 1 Another random sample of n 2   12 regions in the Rocky Mountain states gave the following violent crime rates (per million population)  x 2  Rocky Mountain Crime Rate 3 74 14 75 53 34 83 52 43 13 55 22 8 Assume that the crime rate distribution is approximately normal in both regions  (a) Use a calculator to calculate x 1 , s 1 , x 2 , and s 2   (Round your answers to four decimal places ) x 1   s 1   x 2   s 2   What is the value of the sample test statistic  (Test the difference 1 2   Round your answer to three decimal places ) Q4 In this problem, assume that the distribution of differences is approximately normal  Note   For degrees of freedom d   f   not in the Student's t table, use the closest d   f   that is smaller   In some situations, this choice of d   f   may increase the P  value by a small amount and therefore produce a slightly more  conservative  answer  Are America's top chief executive officers (CEOs) really worth all that money  One way to answer this question is to look at row B , the annual company percentage increase in revenue, versus row A , the CEO's annual percentage salary increase in that same company  Suppose a random sample of companies yielded the following data  B   Percent increase for company 24 25 25 18 6 4 21 37 A   Percent increase for CEO 21 23 24 14 4 19 15 30 Do these data indicate that the population mean percentage increase in corporate revenue (row B ) is different from the population mean percentage increase in CEO salary  Use a 5  level of significance  (Let d   B A  ) What is the value of the sample test statistic  (Round your answer to three decimal places ) Q5 In this problem, assume that the distribution of differences is approximately normal  Note   For degrees of freedom d   f   not in the Student's t table, use the closest d   f   that is smaller   In some situations, this choice of d   f   may increase the P  value by a small amount and therefore produce a slightly more  conservative  answer  At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below  Weather Station 1 2 3 4 5 January  135 120 126 64 78 April 108 115 100 88 61 Does this information indicate that the peak wind gusts are higher in January than in April  Use  0 01  (Let d   JanuaryApril ) What is the value of the sample test statistic  (Round your answer to three decimal places ) Q6 In this problem, assume that the distribution of differences is approximately normal  Note   For degrees of freedom d f  not in the Student's t  table, use the closest d f  that is smaller   In some situations, this choice of d f  may increase the P  value by a small amount and therefore produce a slightly more  conservative  answer  In environmental studies, sex ratios are of great importance  Wolf society, packs, and ecology have been studied extensively at different locations in the U S  and foreign countries  Sex ratios for eight study sites in northern Europe are shown below  Location of Wolf Pack  Males (Winter)  Males (Summer) Finland76 57 Finland51 54 Finland71 55 Lapland55 48 Lapland64 55 Russia50 50 Russia41 50 Russia55 45 What is the value of the sample test statistic  (Round your answer to three decimal places )

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A random sample of n 1 =20winter days in Denver gave a sample mean pollution index x 1 =43. Previous studies show that 1 =11.

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